Mathematics of AC Voltages
Alternating currents are accompanied (or caused) by alternating voltages. An AC voltage v can be described mathematically as a function of time by the following equation:
- ,
where
- is the peak voltage (unit: volt),
- is the angular frequency (unit: radians per second)
- The angular frequency is related to the physical frequency, (unit = hertz), which represents the number of cycles per second, by the equation .
- is the time (unit: second).
The peak-to-peak value of an AC voltage is defined as the difference between its positive peak and its negative peak. Since the maximum value of is +1 and the minimum value is −1, an AC voltage swings between and . The peak-to-peak voltage, usually written as or, is therefore .
Read more about this topic: Alternating Current
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“Why does man freeze to death trying to reach the North Pole? Why does man drive himself to suffer the steam and heat of the Amazon? Why does he stagger his mind with the mathematics of the sky? Once the question mark has arisen in the human brain the answer must be found, if it takes a hundred years. A thousand years.”
—Walter Reisch (1903–1963)